**Circuit Considerations**

Electromagnetic stimulation devices in general are based on a capacitor driving current into the inductance of the stimulator core. A full circuit and a simplified circuit are presented in **Figure 3**.

**Figure 3**

(Full circuit)

(Simplified circuit)

The dc charged capacitor is allowed to resonate a complete cycle, and the core head is where inductance is generated. In a situation without winding resistance, the capacitive energy would shift to inductive energy , and reverse back to the capacitor. The period of time required for a full wavelength can be expressed by .

The inductor core generates a magnetic flux that passes into the biological tissue (i.e. the cortex, in the case of TMS) and induces a voltage through the tissue linked by the flux. Only a fraction of that flux will connect a circuit consisting of the intracellular and extracellular space of a nerve through the membrane wall because the induced voltage is only a fraction of the flux linking the iron core winding. The circuit of the nerve targeted by the magnetic stimulator is shown below in **Figure 4**.

**Figure 4**

During the resting state, the cell membrane is low in permeability (i.e. mobility) to ion flow (mainly Na+). The following model focuses on a subthreshold state over a long nerve length, where capacitance of the membrane wall is expressed in terms of permittivity *ε* for a per unit axial length , radius *r*, and thickness ∆.

Membrane resistance *Rm* is expressed in terms of membrane thickness and membrane wall conductance, *σm*.

And intracellular resistance, *Ri*, per unit length can be written in terms of intracellular conductivity, *σi*, and is significantly greater than the extracellular resistance, which is very small as a result of the extracellular space being very large.

Kent Davey and Epstein C.M.. Magnetic Stimulation Coil and Circuit Design. IEEE Transactions On Biomedical Engineering, Vol. 47, No. 11, November 2000